Minimizing or maximizing the first-passage time to a time-dependent boundary
Mario Lefebvre · Optimization · 2021
Let X(t) be a one-dimensional controlled diffusion process, and Y(t) be a deterministic process. Various models are considered for (X˙(t),Y˙(t)). The optimizer tries to bring the ratio X(t)/Y(t) to a certain value d as soon as possible. There is also a second optimizer whose aim is to prevent the ratio X(t)/Y(t) from reaching d as long as possible. Explicit solutions are obtained. The particular case when the control variables are assumed to be constants and the general case are treated.